Systematic scan for sampling colorings

• 成果类型: Article
• 署名作者: Dyer, M; Goldberg, LA; Jerrum, M
• 署名单位: University of Leeds; University of Warwick; University of Edinburgh
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051605000000683
• 发表日期: 2006
• 页码: 185-230
• 关键词: mixing times; algorithms

摘要

We address the problem of sampling colorings of a graph G by Markov chain simulation. For most of the article we restrict attention to proper q-colorings of a path on n vertices (in statistical physics terms, the one-dimensional q-state Potts model at zero temperature), though in later sections we widen our scope to general H-colorings of arbitrary graphs G. Existing theoretical analyses of the mixing time of such simulations relate mainly to a dynamics in which a random vertex is selected for updating at each step. However, experimental work is often carried out using systematic strategies that cycle through coordinates in a deterministic manner, a dynamics sometimes known as systematic scan. The mixing time of systematic scan seems more difficult to analyze than that of random updates, and little is currently known. In this article we go some way toward correcting this imbalance. By adapting a variety of techniques, we derive upper and lower bounds (often tight) on the mixing time of systematic scan. An unusual feature of systematic scan as far as the analysis is concerned is that it fails to be time reversible.